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TECHNICAL LIBRARY

Modeling Bipolar Devices Using the MEXTRAM Model

Introduction

The MEXTRAM bipolar model was recently released into the public
domain by Philips Electronics N.V. and this model is now supported
by UTMOST and SmartSpice. This article will give a very brief introduction
to the MEXTRAM model. Some measured DC device characteristics will
be modeled with the MEXTRAM equations and the results of this UTMOST
parameter extraction experiment will be shown here.

The MEXTRAM Model

Accurate and reliable simulation of bipolar circuits require that
the circuit simulator model in use can describe a large number of
physical phenomena. The extended Gummel-Poon model, commonly used
by circuit designers, often fails be meet the required accuracy
criteria. The MEXTRAM equations model the following effects:

Temperature effects

Charge storage effects

Substrate effects including the parasitic PNP

High-injection effects

Built-in electric field in base region

Bias-dependent Early effect

Low-level non-ideal base currents

Hard and quasi-saturation

Weak avalanche

Hot carrier effects in the collector epilayer

Explicit modeling of the inactive regions

Split base-collector depletion capacitance

Current crowding and conductivity modulation for base resistance

First-order approximation of distributed high frequency effects
in the intrinsic base (high-frequency current crowding and excess
phase-shift).

Like most other bipolar models MEXTRAM does not contain extensive
geometrical or process scaling rules. A multiplication factor does
exist in the model for parallel transistor arrangements. In total
the MEXTRAM model contains 39 parameters for the modeling of current
and charge, 13 temperature scaling parameters, and 3 parameters
in its noise model. The MEXTRAM model has five internal nodes and
model computing times should be, on average, three times greater
than if the Gummel-Poon model were used. Full details of the model
equations are available elsewhere [1,2].

MEXTRAM Parameter Extraction Example

The following data was measured for an NPN bipolar device:

a) Forward Gummel Data

b) Reverse Gummel Data

c) IC versus VCE at 3 base current levels

d) IE versus VEC at 3 base current levels

The measured data is plotted in Figure 1. Local optimization strategies
were used to extract the required DC parameters from this data.
An entire parameter extraction procedure for the MEXTRAM model using
capacitance, DC, and fT data can be found elsewhere [3] and the
strategies used in this example were based on the DC portion of
this procedure.

Figure 1. A complete measured data set for the NPN
bipolar device.

Four local optimization strategies were implemented for the extraction
of a partial parameter set for the MEXTRAM model. These are described
in Table 1. Some parameter descriptions appear in Table 2.

Strategy

Steps

Parameters

Data

A

4

BF, IS, IBF, VLF

Forward Gummel (low and medium VBE levels)

BF, IK, RBC, RBV,
RE, VBE

Forward Gummel (high and medium levels)

B

4

BRI, ISS, IBR, VLR

Reverse Gummel (low and medium VBC levels)

BRI, IKS, RCC,
XEXT

Reverse Gummel high and medium VBC levels)

C

1

XCJC, BF (refine)

IC versus VCE

D

1

QBO, BRI (refine)

IE versus VEC

Table 1. Details of the UTMOST local optimization
strategies used.

Parameter

Description

IS
BF
IBF
VLF
IK
RBC
RBV
RE
ISS
BRI
IBR
VLR
IKS
RCC
XEXT
XCJC
QB0

Collector-emitter saturation current
Ideal forward gain
Saturation current of the non-ideal forward base current
Cross-over voltage of the non-ideal forward base current
High-injection knee current
Constant part of base resistance
Variable part of base resistance at zero bias
Emitter series resistance
Base-substrate saturation current
Ideal reverse current gain
Saturation current of the non-ideal reverse base current
Cross-over voltage of the non-ideal reverse base current
Knee current of the substrate
Constant part of collector resistance
Partitioning factor
Fraction of collector-base depletion capacitance under the
emitter area
Base charge at zero bias

Table 2. A description of the extracted MEXTRAM
parameters.

Strategy A involves the extraction of parameters to the forward
Gummel characteristics. Using the UTMOST local optimization environment
the collector and base current data was split up into various regions,
four in all, and the associated parameters were extracted. In the
second stage of the extraction procedure a similar analysis was
performed on the reverse Gummel data. At this stage the majority
of the parameters to be extracted to the DC characteristics were
determined. In the final two local optimization strategies the parameters
which model the forward and reverse early effects were extracted
using the IC versus VCE and IE versus VEC data sets respectively.
During these extraction stages the ideal forward and reverse gain
parameters were also refined. The accuracy of the extracted MEXTRAM
model surpasses that of a SPICE Gummel-Poon model derived from the
same data. Improvements were most obvious in the modeling of the
reverse characteristics.

The entire extraction process took less than 1 minute on a Sparc
2 computer and the results were good. Figure 2 shows the measured
and simulated forward characteristics including a plot of the forward
gain versus VBE. Figure 3 shows the measured and simulated reverse
characteristics including a plot of reverse gain versus VBC.

This article has given an introduction to the Philips MEXTRAM bipolar
model which has been implemented into SmartSpice and UTMOST. A very
accurate model of measured device characteristics was obtained very
quickly using some simple user-defined local optimization strategies.

Acknowledgement

SILVACO would like to thank Willy Kloosterman of Philips Research
Laboratories, Eindhoven, The Netherlands, for his help during the
course of this work.